Engineering Calculus Notes 184

Engineering Calculus Notes 184 - t ) + cos t ) k , t = 2...

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172 CHAPTER 2. CURVES (j) ( x 1 ,y 1 ,z 1 ) = (1 , 2 , 3) , ( x n +1 ,y n +1 ,z n +1 ) = ( x n + 1 2 y n ,y n + 1 2 z n , 1 2 z n ) 2. An accumulation point of a sequence { −→ p i } of points is any limit point of any subsequence. Find all the accumulation points of each sequence below. (a) p 1 n , ( 1) n n n + 1 P (b) p n n + 1 cos n, n n + 1 sin n P (c) p n n + 1 , ( 1) n n 2 n + 1 , ( 1) n 2 n n + 1 P (d) p n n + 1 cos 2 , n n + 1 sin 2 , 2 n n + 1 P 3. For each vector-valued function −→ p ( t ) and time t = t 0 below, ±nd the linearization T t 0 −→ p ( t ). (a) −→ p ( t ) = ( t,t 2 ), t = 1 (b) −→ p ( t ) = t 2 −→ ı t 3 −→ , t = 2 (c) −→ p ( t ) = (sin t, cos t ), t = 4 π 3 (d) −→ p ( t ) = (2 t + 1) −→ ı + (3 t 2 2) −→ , t = 2 (e) −→ p ( t ) = (sin t, cos t, 2 t ), t = π 6 (f) −→ p ( t ) = (sin t ) −→ ı + (cos 2
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Unformatted text preview: t ) + cos t ) k , t = 2 Theory problems: 4. Prove the triangle inequality dist( P,Q ) dist( P,R ) + dist( R,Q ) (a) in R 2 ; (b) in R 3 . ( Hint: Replace each distance with its denition. Square both sides of the inequality and expand, cancelling terms that appear on both sides, and then rearrange so that the single square root is on on one side; then square again and move all terms to the same side of the...
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This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.

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